On the control of an unstable periodic state in the repeated fed‐batch operation of a biochemical system

In this paper we discuss the proportional feedback control of a repeated fed‐batch reactor around a desired but unstable periodic state. The flow rate in each cycle is assumed to be a constant. The unstable periodic state is determined using a shooting method technique and its stability is found using the Floquet theory. The control action is based on the performance, i.e., biomass concentration, at the end of the cycle. Two choices of the manipulated variable are investigated, i.e., the cycle time and the flow rate. The concentration of the substrate in the feed is assumed to be a constant.